Method and device for assessing the quality of an optimization-based control signal prior to its use in a technical system

Abstract

A method for assessing the quality of a solution from an optimization process configured to solve a constrained quadratic problem (QP), the method comprising: initiating an execution of an active-set optimization process configured to solve the constrained QP; obtaining a first solution vector and an associated active set of constraints from the execution of the active-set optimization process; substituting variables in the constrained QP in accordance with the active set of constraints to form an associated unconstrained QP; initiating an execution of a second optimization process configured to solve the associated unconstrained QP; obtaining a second solution vector from the execution of the second optimization process; and generating a quality indicator for the first solution vector on the basis of a difference between the first and the second solution vectors.

1 . A computer-implemented method for assessing the quality of a solution from an optimization process configured to solve a constrained quadratic problem (QP) the method comprising:
 initiating an execution of an active-set (AS) optimization process configured to solve the constrained QP;   obtaining a first solution vector and an associated active set of constraints from the execution of the AS optimization process;   substituting variables in the constrained QP in accordance with the active set of constraints to form an associated unconstrained QP, wherein the variable substitution reduces the dimensionality by the number of constraints in the active set;   initiating an execution of a second optimization process configured to solve the associated unconstrained QP;   obtaining a second solution vector from the execution of the second optimization process, including undoing the variable substitution; and   generating a quality indicator for the first solution vector on the basis of a difference between the first and the second solution vectors.   
     
     
         2 . The method of  claim 1 , wherein the difference is related to a vector difference of the first and the second solution vectors. 
     
     
         3 . The method of  claim 1 , wherein:
 the predefined constrained QP includes an optimization of a cost functional; and   the quality indicator is generated further on the basis of the respective costs of the first and the second solution vectors.   
     
     
         4 . The method of  claim 1 , wherein the substitution of variables includes solving for one of the variables of an inequality constraint in the case of equality. 
     
     
         5 . The method of  claim 1 , wherein the AS optimization process and/or the second optimization process is iterative. 
     
     
         6 . The method of  claim 5 , wherein the first solution vector and/or the second solution vector is extracted after a predetermined delay. 
     
     
         7 . The method of  claim 1 , wherein the AS optimization process and the second optimization process are of different types. 
     
     
         8 . The method of  claim 1 , wherein the AS optimization process includes executing one or more selected from the set comprising:
 an interior-point method (IP); alternating direction method of multipliers, (ADMM); successive linear programming (SLP); sequential quadratic programming (SQP); sequential linear-quadratic programming (SLQP); a reduced gradient method (RG).   
     
     
         9 . The method of  claim 1 , wherein the constrained QP relates to control of a technical system, further comprising:
 deciding, on the basis of the quality indicator, whether or not to utilize the first solution vector for generating a control signal to the technical system.   
     
     
         10 . The method of  claim 9 , wherein the constrained QP relates to control of a technical system in real time. 
     
     
         11 . The method of  claim 9 , wherein the technical system is an over-actuated technical system, such as a propulsion system in a road vehicle. 
     
     
         12 . A controller configured to control a technical system in real time, the controller comprising memory, a signal interface, and processing circuitry configured to perform the method of  claim 1 . 
     
     
         13 . A computer program comprising instructions for causing a controller configured to control a technical system in real time, the controller comprising memory, a signal interface, and processing circuitry, to perform the method of  claim 1 .